Question
Given the equation 5 + x -14 = x-7
Part A. Solve the equation 5 + x -14 = x-7
. In your final answer, be sure to state the solution and include all of your work.
Part B. Use the values 2, 0, 3
to verify your solution to the equation 5 + x -14 = x-7
. In your final answer, include all of your calculations.
Part A. Solve the equation 5 + x -14 = x-7
. In your final answer, be sure to state the solution and include all of your work.
Part B. Use the values 2, 0, 3
to verify your solution to the equation 5 + x -14 = x-7
. In your final answer, include all of your calculations.
Answers
GPT-4o mini
Let's solve the equation step by step for Part A.
**Part A: Solve the equation \( 5 + x - 14 = x - 7 \)**
1. **Simplify the left side**:
\[
5 + x - 14 = x - 7
\]
Combine \(5\) and \(-14\):
\[
-9 + x = x - 7
\]
2. **Eliminate \(x\) from both sides**:
Subtract \(x\) from both sides:
\[
-9 = -7
\]
3. **Analyze the result**:
The equation \(-9 = -7\) is a false statement, indicating that there are no values for \(x\) that satisfy this equation.
Therefore, there is no solution to the equation \(5 + x - 14 = x - 7\).
**Final answer for Part A**: No solution.
---
**Part B: Verify the solution using the values \(2\), \(0\), and \(3\)**
Since we concluded in Part A that there is no solution, we can substitute the values of \(2\), \(0\), and \(3\) into the original equation to confirm that they indeed do not satisfy the equation.
1. **Substituting \(x = 2\)**:
\[
5 + 2 - 14 = 2 - 7
\]
Calculate the left side:
\[
5 + 2 - 14 = -7
\]
Calculate the right side:
\[
2 - 7 = -5
\]
Since \(-7 \neq -5\), \(x = 2\) does not satisfy the equation.
2. **Substituting \(x = 0\)**:
\[
5 + 0 - 14 = 0 - 7
\]
Calculate the left side:
\[
5 - 14 = -9
\]
Calculate the right side:
\[
0 - 7 = -7
\]
Since \(-9 \neq -7\), \(x = 0\) does not satisfy the equation.
3. **Substituting \(x = 3\)**:
\[
5 + 3 - 14 = 3 - 7
\]
Calculate the left side:
\[
5 + 3 - 14 = -6
\]
Calculate the right side:
\[
3 - 7 = -4
\]
Since \(-6 \neq -4\), \(x = 3\) does not satisfy the equation.
**Final answer for Part B**: All the tested values (\(2\), \(0\), and \(3\)) do not satisfy the equation \(5 + x - 14 = x - 7\), confirming that there is no solution.
**Part A: Solve the equation \( 5 + x - 14 = x - 7 \)**
1. **Simplify the left side**:
\[
5 + x - 14 = x - 7
\]
Combine \(5\) and \(-14\):
\[
-9 + x = x - 7
\]
2. **Eliminate \(x\) from both sides**:
Subtract \(x\) from both sides:
\[
-9 = -7
\]
3. **Analyze the result**:
The equation \(-9 = -7\) is a false statement, indicating that there are no values for \(x\) that satisfy this equation.
Therefore, there is no solution to the equation \(5 + x - 14 = x - 7\).
**Final answer for Part A**: No solution.
---
**Part B: Verify the solution using the values \(2\), \(0\), and \(3\)**
Since we concluded in Part A that there is no solution, we can substitute the values of \(2\), \(0\), and \(3\) into the original equation to confirm that they indeed do not satisfy the equation.
1. **Substituting \(x = 2\)**:
\[
5 + 2 - 14 = 2 - 7
\]
Calculate the left side:
\[
5 + 2 - 14 = -7
\]
Calculate the right side:
\[
2 - 7 = -5
\]
Since \(-7 \neq -5\), \(x = 2\) does not satisfy the equation.
2. **Substituting \(x = 0\)**:
\[
5 + 0 - 14 = 0 - 7
\]
Calculate the left side:
\[
5 - 14 = -9
\]
Calculate the right side:
\[
0 - 7 = -7
\]
Since \(-9 \neq -7\), \(x = 0\) does not satisfy the equation.
3. **Substituting \(x = 3\)**:
\[
5 + 3 - 14 = 3 - 7
\]
Calculate the left side:
\[
5 + 3 - 14 = -6
\]
Calculate the right side:
\[
3 - 7 = -4
\]
Since \(-6 \neq -4\), \(x = 3\) does not satisfy the equation.
**Final answer for Part B**: All the tested values (\(2\), \(0\), and \(3\)) do not satisfy the equation \(5 + x - 14 = x - 7\), confirming that there is no solution.
can you use less words and make it less advanced
GPT-4o mini
Sure! Let's simplify the explanation.
**Part A: Solve the equation \(5 + x - 14 = x - 7\)**
1. Start with the equation:
\[
5 + x - 14 = x - 7
\]
2. Combine \(5\) and \(-14\) on the left:
\[
-9 + x = x - 7
\]
3. Subtract \(x\) from both sides:
\[
-9 = -7
\]
Since \(-9\) does not equal \(-7\), there is **no solution**.
**Final answer for Part A**: No solution.
---
**Part B: Verify with values \(2\), \(0\), and \(3\)**
1. **For \(x = 2\)**:
\[
5 + 2 - 14 = 2 - 7
\]
Left side: \(5 + 2 - 14 = -7\)
Right side: \(2 - 7 = -5\)
They are not equal.
2. **For \(x = 0\)**:
\[
5 + 0 - 14 = 0 - 7
\]
Left side: \(5 - 14 = -9\)
Right side: \(0 - 7 = -7\)
They are not equal.
3. **For \(x = 3\)**:
\[
5 + 3 - 14 = 3 - 7
\]
Left side: \(5 + 3 - 14 = -6\)
Right side: \(3 - 7 = -4\)
They are not equal.
**Final answer for Part B**: None of the values \(2\), \(0\), or \(3\) work, confirming that there is no solution.
**Part A: Solve the equation \(5 + x - 14 = x - 7\)**
1. Start with the equation:
\[
5 + x - 14 = x - 7
\]
2. Combine \(5\) and \(-14\) on the left:
\[
-9 + x = x - 7
\]
3. Subtract \(x\) from both sides:
\[
-9 = -7
\]
Since \(-9\) does not equal \(-7\), there is **no solution**.
**Final answer for Part A**: No solution.
---
**Part B: Verify with values \(2\), \(0\), and \(3\)**
1. **For \(x = 2\)**:
\[
5 + 2 - 14 = 2 - 7
\]
Left side: \(5 + 2 - 14 = -7\)
Right side: \(2 - 7 = -5\)
They are not equal.
2. **For \(x = 0\)**:
\[
5 + 0 - 14 = 0 - 7
\]
Left side: \(5 - 14 = -9\)
Right side: \(0 - 7 = -7\)
They are not equal.
3. **For \(x = 3\)**:
\[
5 + 3 - 14 = 3 - 7
\]
Left side: \(5 + 3 - 14 = -6\)
Right side: \(3 - 7 = -4\)
They are not equal.
**Final answer for Part B**: None of the values \(2\), \(0\), or \(3\) work, confirming that there is no solution.